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A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential. (English) Zbl 1205.47029

Summary: We consider a discrete Schrödinger operator \(\mathcal J\) with Wigner-von Neumann potential not belonging to \(l^2\). We find the asymptotics of orthonormal polynomials associated to \({\mathcal J}\). We prove a Weyl-Titchmarsh type formula, which relates the spectral density of \({\mathcal J}\) to a coefficient in the asymptotics of the orthonormal polynomials.

MSC:

47B36 Jacobi (tridiagonal) operators (matrices) and generalizations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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